Lower Bounds on Mutual Information

We correct claims about lower bounds on mutual information (MI) between real-valued random variables made in A. Kraskov {\it et al.}, Phys. Rev. E {\bf 69}, 066138 (2004). We show that non-trivial lower bounds on MI in terms of linear correlations depend on the marginal (single variable) distributions. This is so in spite of the invariance of MI under reparametrizations, because linear correlations are not invariant under them. The simplest bounds are obtained for Gaussians, but the most interesting ones for practical purposes are obtained for uniform marginal distributions. The latter can be enforced in general by using the ranks of the individual variables instead of their actual values, in which case one obtains bounds on MI in terms of Spearman correlation coefficients. We show with gene expression data that these bounds are in general non-trivial, and the degree of their (non-)saturation yields valuable insight.Comment: 4 page

Evolving Newton's Constant, Extended Gravity Theories and SnIa Data Analysis

If Newton's constant G evolves on cosmological timescales as predicted by extended gravity theories then Type Ia supernovae (SnIa) can not be treated as standard candles. The magnitude-redshift datasets however can still be useful. They can be used to simultaneously fit for both H(z) and G(z) (so that local G(z) constraints are also satisfied) in the context of appropriate parametrizations. Here we demonstrate how can this analysis be done by applying it to the Gold SnIa dataset. We compare the derived effective equation of state parameter w(z) at best fit with the corresponding result obtained by neglecting the evolution G(z). We show that even though the results clearly differ from each other, in both cases the best fit w(z) crosses the phantom divide w=-1. We then attempt to reconstruct a scalar tensor theory that predicts the derived best fit forms of H(z) and G(z). Since the best fit G(z) fixes the scalar tensor potential evolution F(z), there is no ambiguity in the reconstruction and the potential U(z) can be derived uniquely. The particular reconstructed scalar tensor theory however, involves a change of sign of the kinetic term $\Phi'(z)^2$ as in the minimally coupled case.Comment: Minor changes. Accepted in Phys. Rev. D. 7 revtex pages, 5 figures. The mathematica file with the numerical analysis of the paper is available at http://leandros.physics.uoi.gr/snevol.ht

The Statistics of Crumpled Paper

A statistical study of crumpled paper is allowed by a minimal 1D model: a self-avoiding line bent at sharp angles -- in which resides the elastic energy -- put in a confining potential. Many independent equilibrium configurations are generated numerically and their properties are investigated. At small confinement, the distribution of segment lengths is log-normal in agreement with previous predictions and experiments. At high confinement, the system approaches a jammed state with a critical behavior, whereas the length distribution follows a Gamma law which parameter is predicted as a function of the number of layers in the system

Optimal control technique for Many Body Quantum Systems dynamics

We present an efficient strategy for controlling a vast range of non-integrable quantum many body one-dimensional systems that can be merged with state-of-the-art tensor network simulation methods like the density Matrix Renormalization Group. To demonstrate its potential, we employ it to solve a major issue in current optical-lattice physics with ultra-cold atoms: we show how to reduce by about two orders of magnitudes the time needed to bring a superfluid gas into a Mott insulator state, while suppressing defects by more than one order of magnitude as compared to current experiments [1]. Finally, we show that the optimal pulse is robust against atom number fluctuations.Comment: 5 pages, 4 figures, published versio

Interpreting the High Frequency QPO Power Spectra of Accreting Black Holes

In the context of a relativistic hot spot model, we investigate different physical mechanisms to explain the behavior of quasi-periodic oscillations (QPOs) from accreting black holes. The locations and amplitudes of the QPO peaks are determined by the ray-tracing calculations presented in Schnittman & Bertschinger (2004a): the black hole mass and angular momentum give the geodesic coordinate frequencies, while the disk inclination and the hot spot size, shape, and overbrightness give the amplitudes of the different peaks. In this paper additional features are added to the existing model to explain the broadening of the QPO peaks as well as the damping of higher frequency harmonics in the power spectrum. We present a number of analytic results that closely agree with more detailed numerical calculations. Four primary pieces are developed: the addition of multiple hot spots with random phases, a finite width in the distribution of geodesic orbits, Poisson sampling of the detected photons, and the scattering of photons from the hot spot through a corona of hot electrons around the black hole. Finally, the complete model is used to fit the observed power spectra of both type A and type B QPOs seen in XTE J1550-564, giving confidence limits on each of the model parameters.Comment: 30 pages, 5 figures, submitted to Ap

Pulling adsorbed polymers from surfaces with the AFM: stick versus slip, peeling versus gliding

We consider the response of an adsorbed polymer that is pulled by an AFM within a simple geometric framework. We separately consider the cases of i) fixed polymer-surface contact point, ii) sticky case where the polymer is peeled off from the substrate, and iii) slippery case where the polymer glides over the surface. The resultant behavior depends on the value of the surface friction coefficient and the adsorption strength. Our resultant force profiles in principle allow to extract both from non-equilibrium force-spectroscopic data.Comment: 6 pages, 3 figures; accepted for publication in Europhys. Lett., http://www.edpsciences.org/journal/index.cfm?edpsname=ep

Random matrix description of decaying quantum systems

This contribution describes a statistical model for decaying quantum systems (e.g. photo-dissociation or -ionization). It takes the interference between direct and indirect decay processes explicitely into account. The resulting expressions for the partial decay amplitudes and the corresponding cross sections may be considered a many-channel many-resonance generalization of Fano's original work on resonance lineshapes [Phys. Rev 124, 1866 (1961)]. A statistical (random matrix) model is then introduced. It allows to describe chaotic scattering systems with tunable couplings to the decay channels. We focus on the autocorrelation function of the total (photo) cross section, and we find that it depends on the same combination of parameters, as the Fano-parameter distribution. These combinations are statistical variants of the one-channel Fano parameter. It is thus possible to study Fano interference (i.e. the interference between direct and indirect decay paths) on the basis of the autocorrelation function, and thereby in the regime of overlapping resonances. It allows us, to study the Fano interference in the limit of strongly overlapping resonances, where we find a persisting effect on the level of the weak localization correction.Comment: 16 pages, 2 figure

Infinite qubit rings with maximal nearest neighbor entanglement: the Bethe ansatz solution

We search for translationally invariant states of qubits on a ring that maximize the nearest neighbor entanglement. This problem was initially studied by O'Connor and Wootters [Phys. Rev. A {\bf 63}, 052302 (2001)]. We first map the problem to the search for the ground state of a spin 1/2 Heisenberg XXZ model. Using the exact Bethe ansatz solution in the limit of an infinite ring, we prove the correctness of the assumption of O'Connor and Wootters that the state of maximal entanglement does not have any pair of neighboring spins ``down'' (or, alternatively spins ``up''). For sufficiently small fixed magnetization, however, the assumption does not hold: we identify the region of magnetizations for which the states that maximize the nearest neighbor entanglement necessarily contain pairs of neighboring spins ``down''.Comment: 10 pages, 4 figures; Eq. (45) and Fig. 3 corrected, no qualitative change in conclusion

Functional renormalization group for Luttinger liquids with impurities

We improve the recently developed functional renormalization group (fRG) for impurities and boundaries in Luttinger liquids by including renormalization of the two-particle interaction, in addition to renormalization of the impurity potential. Explicit flow-equations are derived for spinless lattice fermions with nearest neighbor interaction at zero temperature, and a fast algorithm for solving these equations for very large systems is presented. We compute spectral properties of single-particle excitations, and the oscillations in the density profile induced by impurities or boundaries for chains with up to 1000000 lattice sites. The expected asymptotic power-laws at low energy or long distance are fully captured by the fRG. Results on the relevant energy scales and crossover phenomena at intermediate scales are also obtained. A comparison with numerical density matrix renormalization results for systems with up to 1000 sites shows that the fRG with the inclusion of vertex renormalization is remarkably accurate even for intermediate interaction strengths.Comment: 35 pages, 16 figures, revised version as publishe